A conservative legal group specialising in defending businesses accused of discriminating against same-sex couples vowed to redouble its efforts Monday after the US supreme court declined to take up one of the group’s flagship cases.

In Elane Photography v Willock, a New Mexico photographer sued after a state human rights commission fined the photographer for its refusal in 2006 to work a same-sex commitment ceremony. The photographer said that to shoot the ceremony – an unofficial blessing as same-sex weddings were not carried out in the state at the time – would have violated the company’s Christian beliefs. The commission made the photographer pay the legal fees of the couple, Vanessa Willock and Misti Collinsworth.

An appeal of the decision by the photographer found its way to the New Mexico supreme court, which ruled in August 2013 that Elane Photography, run by Jonathan and Elaine Huguenin, had engaged in discriminatory business practices. On Monday the supreme court declined to revisit that decision.

Alliance Defending Freedom, the legal group that took up the photographer’s case, said in a statement that while it was “deeply disappointed the supreme court did not take this opportunity to also affirm Jon and Elaine’s freedom”, it hoped that comparable cases in other states would produce a different result.

Alan Sears, the president of the group and the author of the 2003 book The Homosexual Agenda: Exposing the Principal Threat to Religious Freedom Today, vowed in a video statement to continue to fight specifically on behalf of businesses that provide wedding-related services but do not want to work with same-sex couples.

“Alliance Defending Freedom represents bakers, printers, florists and other freedom-loving Americans across the country,” Sears said. “The trail blazed by Elane Photography will not be in vain.”

The group says on its website that it supports a number of wedding-related business accused of discrimination, including a florist in Washington state, a cake artist in Colorado and a T-shirt printer in Kentucky.

In a high-profile case in late February, Arizona governor Jan Brewer vetoed a state bill that would have cleared the way for businesses to refuse service to customers based on their sexual orientation. Similar legislation has been defeated in Kansas and Idaho.

Willock and Collinsworth, the New Mexico couple, filed a complaint against the photographer after the business declined to work with them specifically because they were a same-sex couple.

After Willock emailed an inquiry to Elaine Huguenin, “Huguenin responded to Willock that Elane Photography photographed only ‘traditional weddings’,” according to the New Mexico supreme court ruling, which continues: “Willock emailed back and asked, ‘Are you saying that your company does not offer your photography services to same-sex couples?’ Huguenin responded, ‘Yes, you are correct in saying we do not photograph same-sex weddings,’ and thanked Willock for her interest."

Same-sex marriages have been legally conducted in New Mexico after the state supreme court ruled last year that nothing in law prevents them. New Mexico was the only state in the union not to specifically permit or prevent same-sex marriage.